Is it possible to get aching and discomfort in your lower abdomen around the time of ovulation?

Yes, the egg is released from one of the ovaries, from a cyst in which it is nurtured and matured (the Graafian follicle) at the time of ovulation. The cyst bursts, allows the egg to escape and then the cyst resorbs. However, it may be painful for a day or two just after ovulation and rarely there can be bleeding from this cyst, causing pain too.